Question: Solve for $x$ and $y$ using elimination. ${-6x-y = -31}$ ${-5x-y = -26}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-6x-y = -31}$ $5x+y = 26$ Add the top and bottom equations together. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-6x-y = -31}\thinspace$ to find $y$ ${-6}{(5)}{ - y = -31}$ $-30-y = -31$ $-30{+30} - y = -31{+30}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 5}$ into $\thinspace {-5x-y = -26}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ - y = -26}$ ${y = 1}$